Chapter Review 357

Chapter Review8Review Key Vocabulary

Review Examples and Exercises

inequality, p. 330solution of an inequality, p. 331

solution set, p. 331graph of an inequality, p. 332

Write the word sentence as an inequality.

1. A number m is less than 5.

2. A number h is at least 12.

3. A number k plus 7 is no more than 19.

4. Three times a number b is greater than 6.

Tell whether the given value is a solution of the inequality.

5. x + 3 ≤ 4; x = 1 6. n − 8 > 3; n = 10

7. 6k < 36; k = 6 8. t —

3 ≥ 5; t = 18

Graph the inequality on a number line.

9. x < 0 10. a ≥ 3 11. n ≤ −1

8.18.1 Writing and Graphing Inequalities (pp. 328–335)

Write the word sentence as an inequality.

a. A number x is more than 9.

A number x is more than 9.

x > 9

An inequality is x > 9.

b. A number r divided by 2 is at most 4.

A number r divided by 2 is at most 4.

r —

2 ≤ 4

An inequality is r —

2 ≤ 4.

Vocabulary Help

358 Chapter 8 Inequalities

8.28.2 Solving Inequalities Using Addition or Subtraction (pp. 336–341)

Solve 1 ≤ x − 4. Graph the solution.

1 ≤ x − 4 Write the inequality.

+ 4 + 4 Add 4 to each side.

5 ≤ x Simplify.

The inequality 5 ≤ x is the same as x ≥ 5.

The solution is x ≥ 5.

Solve the inequality. Graph the solution.

12. x + 1 > 3 13. k − 7 ≤ 0 14. y + 8 ≥ 9

15. 24 < 11 + x 16. 4 ≤ n − 4 17. x − 20 > 24

18. b + 12 ≤ 26 19. s − 1.5 < 2.5 20. 1

— 4

+ m ≤ 1

— 2

Undo the subtraction.

8.38.3 Solving Inequalities Using Multiplication or Division (pp. 344–349)

Solve 7n < 42. Graph the solution.

7n < 42 Write the inequality.

7n

— 7

< 42

— 7

Divide each side by 7.

n < 6 Simplify.

The solution is n < 6.

Undo the multiplication.

−2 −1 0 1 2 3 4 5 6 7 8 9

x ≥ 5

−2 −1 0 1 2 3 4 5 6 7 8 9

n < 6

Solve the inequality. Graph the solution.

21. x ÷ 2 < 4 22. 9n ≥ 63 23. x

— 5

> 10

24. 9 ≥ 3b 25. 10p > 40 26. k

— 4

≥ 15

Chapter Review 359

Solve the inequality. Graph the solution.

27. 4x + 1 < 5 28. n

— 2

− 3 ≤ 9 29. 6w − 4 ≥ 8

30. 18 > t —

5 + 11 31. 3c − 4 ≥ 14 32.

p —

4 + 1 > 1

33. 25 ≥ 7s + 4 34. x

— 9

− 0.7 < 1.3 35. d

— 6

− 1.4 > 0.1

8.48.4 Solving Two-Step Inequalities (pp. 350–355)

a. Solve y

— 3

+ 1 > 6. Graph the solution.

y —

3 + 1 > 6 Write the inequality.

− 1 − 1 Subtract 1 from each side.

y —

3 > 5 Simplify.

y —

3 ⋅ 3 > 5 ⋅ 3 Multiply each side by 3.

y > 15 Simplify.

The solution is y > 15.

−20 −15 −10 −5 0 5 10 15 20 25 30 35

y > 15

b. Solve 10 ≥ 3w − 5. Graph the solution.

10 ≥ 3w − 5 Write the inequality.

+ 5 + 5 Add 5 to each side.

15 ≥ 3w Simplify.

15

— 3

≥ 3w

— 3

Divide each side by 3.

5 ≥ w Simplify.

The solution is w ≤ 5.

−2 −1 0 1 2 3 4 5 6 7 8 9

w ≤ 5

Undo the addition.

Undo the division.

Undo the subtraction.

Undo the multiplication.